Changing the orientation of the head with regard to gravity causes a dramatic change in ocular compensatory movements generated by the visual and vestibular systems. We have recently formulated a three dimensional model of how the central nervous system integrates information from the semicircular canals, visual system and otoliths to explain compensatory eye movements in response to rotations about arbitrary axes in a gravitational environment. We have also shown that gravity has the effect of orienting the principal axes of velocity storage toward the spatial vertical. The aim of this research is to mathematically characterize the velocity storage integrator in three dimensions as a function of gravity to predict these changes in orientation. We also intend to characterize the various dynamical system operators in the model that couple to the velocity storage integrator. Specifically, we will determine the eigenvalues and eigenvectors of the velocity storage integrator for a wide range of orientations of the head with regard to gravity. This will be done by giving oblique optokinetic stimuli for a given position of the head and determining the angle relative to the head where the optokinetic after-nystagmus (OKAN) declines along a straight line in velocity space. This will be the eigenvector. The eigenvalue associated with this eigenvector would be the inverse of the time constant of the decay in OKAN. We will also give off-vertical axis rotation about arbitrary angles through the head to determine the optimal planes for generating compensatory eye velocity in three dimensions. Acitivity will be recorded extracellularly from second order vertical as well as horizontal semicircular canal related units in the vestibular nuclei during and after oblique optokinetic nystagmus and optokinetic after-nystagmus. We propose to determine the role of these units in coding the eigenvectors and eigenvalues of velocity storage and in generating the three components of eye velocity during these type of stimuli. We will also test these units during off-vertical axis rotatation about different axes through the head to determine the optimal planes for estimating head velocity generated by the otoliths. Experimental findings will be related to the three dimensional model of the vestibulo- ocular reflex. This research should give a better understanding of how compensatory eye movements are generated during complex head movements. It should also elucidate the functional role of the velocity storage integrator in generating these movements.